Sphere Recognition: Heuristics and Examples
نویسندگان
چکیده
Heuristic techniques for recognizing PL spheres using the topological software polymake are presented. These methods have been successful very often despite sphere recognition being known to be hard (for dimensions d ≥ 3) or even undecidable (for d ≥ 5). A deeper look into the simplicial complexes for which the heuristics failed uncovered a trove of examples having interesting topological and combinatorial properties.
منابع مشابه
Heuristics for Sphere Recognition
The problem of determining whether a given (finite abstract) simplicial complex is homeomorphic to a sphere is undecidable. Still, the task naturally appears in a number of practical applications and can often be solved, even for huge instances, with the use of appropriate heuristics. We report on the current status of suitable techniques and their limitations. We also present implementations i...
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متن کاملStatement of Research
I am a doctoral student working under the supervision of Dr. Frank Lutz at the Technische Universität Berlin in Germany. In my doctoral thesis I describe the construction of some triangulated manifolds we built by hand. We applied heuristic programs to compute certain topological properties of these simplicial complexes to verify that our construction is correct. In doing so we exposed flaws in...
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